Avoid lossless audio containers. h.264/x.264 is a pretty universal video standard, but codecs such as FLAC and AAC are not. The more common AC3 and MP3 codecs are better choices for audio codecs.
As per reducing filesize, there are a bunch of different things you can do to get the file size lower depending on what you deem "substantial quality". Using different encoding methods, reducing sample rate, and dropping resolution are all ways to drop file size down considerably.
This applies to both video and audio by the way. It may be more beneficial to try this with audio first if you're not planning on using headphones since the drop in quality won't be very noticeable through speakers.